Can you change an old 30A fuse box if it has 1r1b1w wire to a 15A gfci for a whirlpool tub outlet?

Yes you can. It involves working in the breaker box and changing out breakers. You'll also have to "re-identify" the black wire to green for your ground.

If you think you can do this, post back and I'll provide details on how.

Yes I Can! The fuse box has 2 30amp fuses.

At the breaker box you'll need a single 15amp breaker. YOU CANNOT USE THE EXISTING 30AMP BREAKER! Attach the black wire to the new breaker and the white wire to the neutral bus (where all the other whites are attached). You now have a red wire remaining. You'll use this as the ground wire. YOU MUST perform what is called "re-identifying" the wire by wrapping green tape around the wire. This lets someone know that the wire is a ground wire and not a hot wire (red is hot, green is ground). Attach this wire to the ground bus (where all the bare copper wires are).

Wiring the GFCI is just like a standard receptacle (black and white on the terminals and your RED (which has now become a ground wire) on the green ground screw. Make sure to wrap the red wire with green tape at the GCFI also! This is very important!